List of top Mathematics Questions

Two bags: A (2W, 3R), B (4W, 5R). One red drawn. Find probability it came from B.
50 people, 20 always tell truth.Two selected. Find probability distribution of number of truth-tellers.
Find the integral:
\[ I = \int \frac{\cos \theta \, d\theta}{\sqrt{3 - 3\sin \theta - \cos^2 \theta}} \]
Find: \[ I = \int \frac{2x^2 + 1}{x^2(x^2 + 4)} \, dx \]
Find the particular solution of the differential equation:
\[ \frac{dy}{dx} = \frac{xy}{x^2 + y^2} \] given that \( y = 1 \) when \( x = 0 \).
Find the particular solution of: \[ (1 + x^2) \frac{dy}{dx} + 2xy = \frac{1}{1 + x^2}, y = 0 \text{ when } x = 1. \]
Evaluate: \[ I = \int_{0}^{\pi/2} \frac{ x \sin x \cos x }{ \sin^4 x + \cos^4 x } \, dx. \]
If \( |\vec{a}| = 7 \), \( |\vec{b}| = 24 \), \( |\vec{c}| = 25 \) and
\( \vec{a} + \vec{b} + \vec{c} = \vec{0} \),
find the value of \( \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a} \).
If a line makes angles \( \alpha, \beta, \gamma \) with the x-axis, y-axis, and z-axis respectively,
then prove that: \[ \sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = 2 \]
Prove that the greatest integer function f : R → R, given by f(x) = [x], is neither one-one nor onto
Find the intervals in which the function
\( f(x) = x^4 - 4x^3 + 4x^2 + 15 \) is increasing .

Simplify:
\( \tan^{-1} \left( \frac{\cos x}{1 - \sin x} \right) \)

If $x = a \cos \theta + b \sin \theta$, $y = a \sin \theta - b \cos \theta$, then which one is true?
Assertion (A): The principal value of $\cot^{-1}(\sqrt{3})$ is $\frac{\pi}{6}$.
Reason (R): Domain of $\cot^{-1} x$ is $\mathbb{R} - \{-1, 1\}$.
The corner points of the bounded feasible region of an LPP are O(0, 0), A(250, 0), B(200, 50) and C(0, 175). If the maximum value of the objective function $Z = 2ax + by$ occurs at the points A(250, 0) and B(200, 50), then the relation between a and b is:
corner points of the bounded
If $(\cos x)^y = (\cos y)^x$, then $\frac{dy}{dx}$ is:
The point which lies in the half-plane $2x + y - 4 \le 0$ is:
If $\vec{a}$, $\vec{b}$ and $(\vec{a} + \vec{b})$ are all unit vectors and $\theta$ is the angle between $\vec{a}$ and $\vec{b}$, then the value of $\theta$ is:
The projection of vector $\hat{i}$ on the vector $\hat{i} + \hat{j} + 2\hat{k}$ is:
The vector equation of a line which passes through the point (2, -4, 5) and is parallel to the line $\displaystyle \frac{x+3}{3} = \frac{4-y}{2} = \frac{z+8}{6}$ is:
For which value of x, are the determinants \[ \begin{vmatrix} 2x & -3 \\ 5 & x \end{vmatrix} \text{and} \begin{vmatrix} 10 & 1 \\ -3 & 2 \end{vmatrix} \text{ equal?} \]
The value of the cofactor of the element of second row and third column in the matrix \[ \begin{bmatrix} 4 & 3 & 2 \\ 2 & -1 & 0 \\ 1 & 2 & 3 \end{bmatrix} \text{ is:} \]
A family has 2 children and the elder child is a girl. The probability that both children are girls is:
The value of $\displaystyle \int_{0}^{\pi/6} \sin 3x \, dx$ is:
Let tan-1 x ∈(\(-\frac π2\) \(\frac π2\))  for x ∈ R. Then the number of real solutions of the equation \(\sqrt{1 + \cos (2x)} = \sqrt2 \tan^{-1}(\tan x)\) in the set \((-\frac{3π}{2}, -\frac{π}{2}) ∪ (-\frac{π}{2},\frac{π}{2}) ∪ (\frac{π}{2},\frac{3π}{2})\) is equal to